For constructing the working class consumer price index number of a particular town, the following weights corresponding to different group of items were assigned : Food – $55$, Fuel – $15$, Clothing – $10$, Rent – $8$ and Miscellaneous – $12$. It is known that the rise in food prices is double that of fuel and the rise in miscellaneous group prices is double that of rent. In October $2006$, the increased $\text{D, A}$ by a factory of that town by $182\%$ fully compensated for the rise in prices of food and rent but did not compensate for anything else. Another factory of the same locality increased $\text{D, A}$ by $46.5\%$, which compensated for the rise in fuel and miscellaneous groups.
Which is the correct combination of the rise in prices of food, fuel, rent and miscellaneous group?
- $320.14,159.57,95.64,166.82$
- $317.14,158.57,94.64,189.28$
- $311.14,159.57,90.64,198.28$
- $321.14,162.57,84.46,175.38$